Not sure if I'm right, but do you ever take it off the charger then, and just use it elsewhere?
We both have a 3rd Gen iPad, and once they're charged, they stay well away from the dock, until they're around 20% or so. I'm no expert on charging issues, but just 'feel' that a constant connection isn't a good option, but that's just a personal observation...
We also cleared out a lot of dross (old apps etc.),on both ours, and then did a 'soft reset', which made them go so much better as well!